Insurance & Actuarial Risk

In this work, we address the optimal retirement problem in the presence of a stochastic wage, formulated as a free boundary problem. Specifically, we explore an incomplete market setting where the wage cannot be perfectly hedged through investments in the risk-free and risky assets that characterize

There is little disagreement among insurance actuaries and financial economists about the societal benefits of longevity-risk pooling in the form of life annuities, defined benefit pensions, self-annuitization funds, and even tontine schemes. Indeed, the discounted value or cost of providing an inco

This paper investigates the consumption and investment decisions of an individual facing uncertain lifespan and stochastic labor income within a Black-Scholes market framework. A key aspect of our study involves the agent’s option to choose when to acquire life insurance for bequest purposes. We exa

We study an optimal stopping problem with an unbounded, time-dependent and discontinuous reward function. This problem is motivated by the pricing of a variable annuity contract with guaranteed minimum maturity benefit, under the assumption that the policyholder’s surrender behaviour maximizes the r

The geometric approach to financial markets with proportional transaction cost prescribes to imbed a specific model (of stock market, of currency market etc.), usually given in a parametric form, into a natural framework defined by the two random processes, S and K. The first one, d-dimensional, mod

This article proposes a new class of risk-sharing rules by exploring the relationship between capital allocation and risk sharing. While the former is concerned with ex-ante allocating capitals to different lines of business within a corporation based on the relationship among the individual risks,

We study a monopolistic insurance market with hidden information, where the agent’s type $θ$ is private information that is unobservable to the insurer, and it is drawn from a continuum of types. The hidden type affects both the loss distribution and the risk attitude of the agent. Within this frame

Universal basic income (UBI) is a tax scheme that uniformly redistributes aggregate income amongst the entire population of an economy. We prove the existence of an equilibrium in a model that implements universal basic income. The economic agents choose the proportion of their time to work and earn

In this paper, we provide extended convolution bounds for the Fréchet problem and discuss related implications in quantitative risk management. First, we establish a new form of inequality for the Range-Value-at-Risk (RVaR). Based on this inequality, we obtain bounds for robust risk aggregation with

We introduce a generalized version of Orlicz premia, based on possibly non-convex loss functions. We show that this generalized definition covers a variety of relevant examples, such as the geometric mean and the expectiles, while at the same time retaining a number of relevant properties. We establ

The extreme cases of risk measures, when considered within the context of distributional ambiguity, provide significant guidance for practitioners specializing in risk management of quantitative finance and insurance. In contrast to the findings of preceding studies, we focus on the study of extreme

We consider a model of a reinsurance market consisting of multiple insurers on the demand side and multiple reinsurers on the supply side, thereby providing a unifying framework and extension of the recent literature on optimality and equilibria in reinsurance markets. Each insurer has preferences r

This paper studies the dividend and capital injection problem under a diffusion risk model with general discount functions. A proportional cost is imposed when injecting capitals. For exponential discounting as time-consistent benchmark, we obtain the closed-form solutions and show that the optimal

This paper introduces the class of multidimensional self-exciting processes with dependencies (MSPD), which is a unifying writing for a large class of processes: counting, loss, intensity, and also shifted processes. The framework takes into account dynamic dependencies between the frequency and the

This paper studies an optimal reinsurance problem for a utility-maximizing insurer, subject to the reinsurer’s endogenous default and background risk. An endogenous default occurs when the insurer’s contractual indemnity exceeds the reinsurer’s available reserve, which is random due to the backgroun

We study risk sharing among agents with preferences modeled by heterogeneous distortion risk measures, who are not necessarily risk averse. Pareto optimality for agents using risk measures is often studied through the lens of inf-convolutions, because allocations that attain the inf-convolution are

In this paper, we study the risk sharing problem among multiple agents using Lambda Value-at-Risk as their preference functional, under heterogeneous beliefs, where beliefs are represented by several probability measures. We obtain semi-explicit formulas for the inf-convolution of multiple Lambda Va

In risk-sharing markets with aggregate uncertainty, characterizing Pareto-optimal allocations when agents might not be risk averse is a challenging task, and the literature has only provided limited explicit results thus far. In particular, Pareto optima in such a setting may not necessarily be como

We investigate the optimal reinsurance problem in a risk model with jump clustering features. This modeling framework is inspired by the concept initially proposed in Dassios and Zhao (2011), combining Hawkes and Cox processes with shot noise intensity models. Specifically, these processes describe

We study a reinsurance Stackelberg game in which both the insurer and the reinsurer adopt the mean-variance (abbr. MV) criterion in their decision-making and the reinsurance is irreversible. We apply a unified singular control framework where irreversible reinsurance contracts can be signed in both